We report results from a pilot program to obtain spectroscopy for objects detected in the Galaxy Evolution Explorer (GALEX) Medium Imaging Survey (MIS). Our study examines the properties of galaxies detected by GALEX fainter than the Sloan Digital Sky Survey (SDSS) spectroscopic survey. This is the first study to extend the techniques of Salim and coworkers to estimate stellar masses, star formation rates (SFRs), and the b (star formation history) parameter for star-forming galaxies out to z~0.7. We obtain redshifts for 50 GALEX MIS sources reaching NUV=23.9 (AB mag) having counterparts in the SDSS Data Release 4 (DR4). Of our sample, 43 are star-forming galaxies with z<0.7, 3 have emission-line ratios indicative of active galactic nuclei with z<0.7, and 4 objects with z>1 are QSOs, 3 of which are not previously cataloged. We compare our sample to a much larger sample of ~50000 matched GALEX/SDSS galaxies with SDSS spectroscopy; while our survey is shallow, the optical counterparts to our sources reach ~3mag fainter in SDSS r than the SDSS spectroscopic sample. We use emission-line diagnostics for the galaxies to determine that the sample contains mostly star-forming galaxies.